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<title>Problem 2137. -- submultiple -- 衡阳八中OJ离线版-2012-02-29</title><center><h2>2137: submultiple</h2><span class=green>Time Limit: </span>10 Sec&nbsp;&nbsp;<span class=green>Memory Limit: </span>259 MB<br><span class=green>Submit: </span>25&nbsp;&nbsp;<span class=green>Solved: </span>16<br>[<a href='submitpage.php?id=2137'>Submit</a>][<a href='problemstatus.php?id=2137'>Status</a>][<a href='bbs.php?id=2137'>Discuss</a>]</center><h2>Description</h2><div class=content><p>设函数g(N)表示N的约数个数。现在给出一个数M，求出所有M的约数x的g(x)的K次方和。</p></div><h2>Input</h2><div class=content><p>第一行输入N，K。N表示M由前N小的素数组成。接下来N行，第i+1行有一个正整数Pi，表示第Ai小的素数 有 Pi次。等式：</p></div><h2>Output</h2><div class=content><p>输出一个数，表示答案。只需输出最后答案除以1000000007的余数。</p></div><h2>Sample Input</h2>
			<div class=content><span class=sampledata>2 3<br />
1<br />
3<br />
</span></div><h2>Sample Output</h2>
			<div class=content><span class=sampledata>900<br />
【样例说明】<br />
M=2^1*3^3=54<br />
M的约数有1,2,3,6,9,18,27,54.约数个数分别为1,2,2,4,3,6,4,8.<br />
Answer=1^3+2^3+2^3+4^3+3^3+6^3+4^3+8^3=900<br />
<br />
<br />
编号	N	K	Pi<=<br />
1	50	3	10000<br />
2	50	100	10000<br />
3	50	20101125	10000<br />
4	999	17651851	100000<br />
5	5000	836954247	100000<br />
6	4687	1073741823	100000<br />
7	4321	123456789	100000<br />
8	5216	368756432	100000<br />
9	8080	2^31-1	100000<br />
10	10086	3	2^63-1<br />
11	64970	3	2^63-1<br />
12	71321	3	2^63-1<br />
13	350	5	2^31-1<br />
14	250	6	2^31-1<br />
15	110	7	2^31-1<br />
16	99	8	2^31-1<br />
17	80	9	2^31-1<br />
18	70	10	2^31-1<br />
19	60	11	2^31-1<br />
20	50	12	2^31-1<br />
</span></div><h2>HINT</h2>
			<div class=content><p></p></div><h2>Source</h2>
			<div class=content><p><a href='problemset.html?search=By 梁健楠'>By 梁健楠</a></p></div><center>[<a href='submitpage.php?id=2137'>Submit</a>][<a href='problemstatus.php?id=2137'>Status</a>][<a href='bbs.php?id=2137'>Discuss</a>]</center>﻿<br>

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